Question

Lagrange's four-square theorem states that every positive integer can be written as the sum of four or

fewer square numbers. For instance, 23 - 32+32 +22+12 and 30 -5° +2° +1°. Write each
of the following integers as the sum of four or fewer square numbers.
a. 15
b. 24
0.33
d. any 3-digit, positive integer of your choosing

Answer 1

• 15 = 3² +2² +1² +1²
• 24 = 4² +2² +2²
• 33 = 4² +4² +1²
• 624 = 22² +10² +6² +2²

Explanation:

It doesn't always work to choose the largest possible square first.

a. 15 = 9 + 4 + 1 + 1 = 3² +2² +1² +1²

b. 24 = 16 + 4 + 4 = 4² +2² +2²

c. 33 = 25 + 4 + 4 = 5² +2² +2²

d. 624 = 484 +100 +36 +4 = 22² +10² +6² +2²